Solve for $x$, $ -\dfrac{4x}{2x} = \dfrac{4}{10x} + \dfrac{10}{4x} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $2x$ $10x$ and $4x$ The common denominator is $20x$ To get $20x$ in the denominator of the first term, multiply it by $\frac{10}{10}$ $ -\dfrac{4x}{2x} \times \dfrac{10}{10} = -\dfrac{40x}{20x} $ To get $20x$ in the denominator of the second term, multiply it by $\frac{2}{2}$ $ \dfrac{4}{10x} \times \dfrac{2}{2} = \dfrac{8}{20x} $ To get $20x$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ \dfrac{10}{4x} \times \dfrac{5}{5} = \dfrac{50}{20x} $ This give us: $ -\dfrac{40x}{20x} = \dfrac{8}{20x} + \dfrac{50}{20x} $ If we multiply both sides of the equation by $20x$ , we get: $ -40x = 8 + 50$ $ -40x = 58$ $ -40x = 58 $ $ x = -\dfrac{29}{20}$